The Excel BETA.DIST Function

Basic Description

The Excel BETA.DIST function calculates the cumulative beta distribution function or the beta
probability density function, for a supplied set of parameters.

The function was first introduced in Excel 2010 and so is not available in earlier versions of Excel.
However, earlier versions of Excel do have the
BETADIST function, which
also calculates the cumulative beta distribution, but with slightly less accuracy.

The format of the Beta.Dist function is :

BETA.DIST( x, alpha, beta, cumulative, [A], [B] )

Where the function arguments are:

x

-

The value at which the function is to be calculated (must be between [A] and [B])

alpha

-

A parameter of the distribution (must be > 0)

beta

-

A parameter of the distribution (must be > 0)

cumulative

-

A logical argument that specifies the type of distribution to be used. This can be either:

TRUE

=

Cumulative Beta Distribution Function

FALSE

=

Beta Probability Density Function

[A]

-

An optional argument which gives the lower bound of the interval of x

(if omitted, [A] takes the default value 0)

[B]

-

An optional argument which gives the upper bound of the interval of x

(if omitted, [B] takes the default value 1)

If the arguments [A] and [B] are set to 0 and 1 respectively, this is the Standard Beta Distribution.

Beta.Dist Function Examples

Cumulative Beta Distribution Function Example

Standard Cumulative Beta Distribution Function with α = 4 and β = 5

The above chart on the right shows the Cumulative
Beta Distribution with the parameter alpha set to 4 and the parameter beta set to 5.

The interval of x is set to [0, 1], which makes this the Standard Cumulative Beta Distribution.

If you want to use Excel to calculate the value of this function at x = 0.4, this can be done with
the Beta.Dist function, as follows:

=BETA.DIST( 0.4, 4, 5, TRUE, 0, 1 )

This gives the result 0.4059136.

Beta Probability Density Function Example

Standard Beta Probability Density Function with α = 4 and β = 5

The above chart on the right shows the Beta
Probability Density Function with the parameters alpha and beta set to 4 and 5 respectively.

Again, the interval of x is set to [0, 1], which makes this the Standard Beta Probability Density Function.

If you want to use Excel to calculate the value of this function at x = 0.6, this can be done with
the Beta.Dist function, as follows:

=BETA.DIST( 0.6, 4, 5, FALSE, 0, 1 )

This gives the result 1.548288.

In both of the above examples, the arguments [A] and [B] have been supplied to both functions as the values 0 and 1.
However, these values could have been omitted from the functions, as they would have then taken on the default values of 0 and 1.